Home
Class 11
PHYSICS
A unifrom metallic ring of mass m, rad...

A unifrom metallic ring of mass `m`, radisus `R`, cross sectional area `'a'` and young'/s modulus `Y` kis kept on a smooth cone of radius `2R` and semivertex angle `45^(@)` as shown. [Assume that extension in the ring is small]

A

The tension in the ring will be same through out

B

The tension in the ring will be independent of radius of ring.

C

The extension in the ring will be `(mgR)/(aY)`

D

Elastic potential energy should in the ring will be `(m^(2) g^(2) R)/(8pi Ya)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`2T sin ((d theta)/(2)) = (N)/(sqrt(2)) = dm xx g`
or `T d theta = (M)/(2pi R) (R d theta)g` or `T = (Mg)/(2pi)`
Elonagation `= (T)/(aY) xx 2pi R = (MgR)/(aY)`
Energy `= (1)/(2) xx "stress" xx "strain" xx "volume" = (m^(2) g^(2))/(8pi^(2) a^(2) Y)`
Promotional Banner

Topper's Solved these Questions

  • MECHANICAL PROPERTIES OF SOLIDS

    NARAYNA|Exercise COMPREHENSION TYPE|11 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

    NARAYNA|Exercise SINGLE ANSWER TYPE QUESTIONS|13 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

    NARAYNA|Exercise SINGLE ANSWER TYPE|15 Videos

  • MECHANICAL PROPERTIES OF FLUIDS

    NARAYNA|Exercise EXERCISE - III|30 Videos

  • MOTION IN A PLANE

    NARAYNA|Exercise Level-II(H.W)|31 Videos

Similar Questions

Explore conceptually related problems

A uniform ring having mass m, radius R, cross section area of the wire A and young’s modulus Y is rotating with an angular speed omega ( omega is small) on a smooth horizontal surface. Which of the following options is correct :

A ring of radius R is made of a thin wire of material of density rho , having cross-section area a and Young's modulus y. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is omega . The tension in the ring will be

If a metal wire of length L, having area of cross-section A and young' s modulus Y . Behave as a spring of spring constant K. The value of K is

A metal ring of initial radius r and cross-sectional area A is fitted onto a wooden disc of radius R > r. If Youngs modules of metal is Y then tension in the ring is

Find out the elongation in block. If mass area of cross-section and young modulus of block are m, A and y respectively.

A smooth uniform, string of natural length l , cross-sectional area A and Young’s modulus Y is pulled along its length by a force F on a horizontal surface. Find the elastic potential energy stored in the string.

A stone of mass m is attached to one end of a wire of cross-sectional area A and Young's modulus Y. The stone is revolved in a horizontal circle at a speed such that the wire makes an angle theta with the vertical. The strain produced in the wire will be

Knowledge Check

  • A ring of radius R is made of a thin wire of material of density rho , having cross-section area a and Young's modulus y. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is omega . The tension in the ring will be

    A
    `(arhoR^(2)omega^(2))/(2)`
    B
    `a rho R^(2) omega^(2)`
    C
    `2a rho R^(2) omega^(2)`
    D
    `(arhoR^(2) omega^(2))/(4)`

  • If a metal wire of length L, having area of cross-section A and young' s modulus Y . Behave as a spring of spring constant K. The value of K is

    A
    `(YA)/(L)`
    B
    `(YA)/(2L)`
    C
    `(2YA)/(L)`
    D
    `(YL)/(A)`

  • A ring of mass m and radius R rests in equilibrium on a smooth cone of semi-vertical angle 45^(@) as shown. The radius of the cone is 2R. the radius of circular cross section of the ring is r(r lt lt R) . What will be the tension in the ring?

    A
    `(mg)/(2sqrt(2)pi)`
    B
    `(mg)/(2pi)`
    C
    `(mg)/(sqrt(2)pi)`
    D
    `(sqrt(2)mg)/(pi)`